Eigenframe Curvature from Foam Cell Geometry: A First-Principles Derivation with Falsifiable Gravitational Wave Predictions

The Selection-Cost Framework (SCF) predicts that spacetime possesses a foam microstructure obeying Plateau’s law, with observable consequences encoded in the eigenframe curvature κ = ∥∇P∥ 4/g. We derive the radial profile κ(r) near a Kerr black hole from first principles, starting from tidal distortion of foam cells and proceeding through three distinct contributions to the projection gradient: smooth distortion, T1 topological transitions, and frame-dragginginduced eigenframe rotation. The derivation introduces a single dimensionless coupling constant αfoam = η/β2 = 0.0749, determined entirely by the information retention ratio η = 15.53% andthe Plateau scaling β = 1.44, both independently validated. We present two model-independent predictions: (1) the foam structural relaxation timescale satisfies τκ/τQNM = β = 1.44, a topological result depending only on Plateau angles, and (2) a spin-dependent phase transition at a/M ≈ 0.78 where frame dragging breaks the overlap degeneracy between quasi-normal mode overtones. For GW250114 (62.7 M⊙, a/M ≈ 0.69), the predicted foam relaxation frequency is 28.5 Hz with timescale τκ = 5.58 ms. We identify four falsification tests with detection horizons spanning current LIGO operations through next-generation detectors.